# Post-Minkowskian solution for the small-deflection motion of test particles in Kerr-Newman spacetime

## TL;DR

This paper derives a second-order post-Minkowskian analytical solution describing how test particles, including photons, move in the gravitational field of a Kerr-Newman black hole, accounting for small deflections.

## Contribution

It provides the first explicit second-order post-Minkowskian solution for test particle motion in Kerr-Newman spacetime using an iterative method.

## Key findings

- Explicit formulas for particle trajectories and velocities are obtained.
- Results apply to both massive particles and photons.
- The solution enhances understanding of gravitational deflections in Kerr-Newman spacetime.

## Abstract

We derive the second-order post-Minkowskian solution for the small-deflection motion of test particles in the external field of the Kerr-Newman black hole via an iterative method. The analytical results are exhibited in the coordinate system constituted by the particles' initial velocity unit vector, impact vector, and their cross-product. The achieved formulas explicitly give the dependences of the particles' trajectory and velocity on the time once their initial position and velocity are specified, and can be applied not only to a massive particle, but also to a photon as well.